Apparatus having an array of piezoelectric film sensors for measuring parameters of a process flow within a pipe

ABSTRACT

A apparatus  10,110,170  is provided that measures the speed of sound and/or vortical disturbances propagating in a single phase fluid flow and/or multiphase mixture to determine parameters, such as mixture quality, particle size, vapor/mass ratio, liquid/vapor ratio, mass flow rate, enthalpy and volumetric flow rate of the flow in a pipe, by measuring acoustic and/or dynamic pressures. The apparatus includes a spatial array of unsteady pressure sensors  15 - 18  placed at predetermined axial locations x 1 -x N  disposed axially along the pipe  14.  The pressure sensors  15 - 18  provide acoustic pressure signals P 1 (t)-P N (t) to a signal processing unit  30  which determines the speed of sound a mix  propagating through of the process flow  12  flowing in the pipe  14.  The pressure sensors are piezoelectric film sensors that are mounted or clamped onto the outer surface of the pipe at the respective axial location.

CROSS-REFERENCE TO RELATED PATENT APPLICATIONS

This application is a continuation-in-part of U.S. patent applicationSer. No. 10/712,833, filed Nov. 12, 2003, which claims the benefit ofU.S. Provisional Application No. 60/425,436, filed Nov. 12, 2002; andU.S. Provisional Application No. 60/426,724, filed Nov. 15, 2002; and isa continuation-in-part of U.S. patent application Ser. No. 10/412,839,filed Apr. 10, 2003, which claims the benefit of U.S. ProvisionalApplication No. 60/371,606 filed Apr. 10, 2002, U.S. ProvisionalApplication No. 60/427,964 filed Nov. 20, 2002, and U.S. ProvisionalApplication No. 60/451,375 filed Feb. 28, 2003; and which is acontinuation-in-part of U.S. patent application Ser. No. 10/376,427filed Feb. 26, 2003, which claimed the benefit of U.S. ProvisionalApplication No. 60/359,785, filed Feb. 26, 2002; and which is acontinuation-in-part of U.S. patent application Ser. No. 10/349,716filed Jan. 23, 2003, which claims the benefit of U.S. ProvisionalApplication No. 60/351,232 filed Jan. 23, 2002; U.S. ProvisionalApplication No. 60/359,785 filed Feb. 26, 2002; U.S. ProvisionalApplication No. 60/375,847 filed Apr. 24, 2002; U.S. ProvisionalApplication No. 60/425,436 filed Nov. 12, 2002; and U.S. ProvisionalApplication No. 60/426,724, filed Nov. 15, 2002, all of which areincorporated herein by reference in their entirety.

TECHNICAL FIELD

This invention relates to an apparatus for measuring the parameters of asingle phase and/or multiphase flow, and more particularly to anapparatus having an array of piezoelectric film sensors clamped ormounted onto a process flow pipe for measuring the speed of sound and/orvortical disturbances propagating in a single phase and/or multiphaseflow to determine parameters, such as mixture quality, particle size,vapor/mass ratio, liquid/vapor ratio, mass flow rate, enthalpy andvolumetric flow rate of the flow in the pipe, for example, by measuringacoustic and/or dynamic pressures.

BACKGROUND ART

Numerous technologies have been implemented to measure volumetric andmass flow rates of fluids in industrial processes. Some of the morecommon approaches are based upon ultrasonic time of flight and/orDoppler effects, Coriolis effects, rotating wheels, electromagneticinduction, and pressure differentials. Each of these techniques hascertain drawbacks. For example, invasive techniques that rely oninsertion of a probe into the flow, or geometry changes in the pipe, maybe disruptive to the process and prone to clogging. Other methods suchas ultrasonics may be susceptible to air or stratified flow. Meters thatuse rotating wheels or moving parts are subject to reliability issues.Coriolis meters are limited when pipe diameters become large due to theincrease in force required to vibrate the pipe.

One such process fluid is a saturated vapor/liquid fluid mixture (e.g.,steam). It would be advantageous to be able to measure the vapor qualityof this fluid mixture. Vapor quality of a saturated vapor/liquid mixtureis defined as ratio of the mass of the vapor phase to the total mass ofthe mixture. Saturated mixtures exist at temperatures and pressures atwhich liquid and vapor phases coexist. The temperatures and pressures atwhich the liquid and vapor phases coexist lie under the “vapor bubble”on a phase diagram. The collection of points known as the saturatedliquid line and the collections of points known as the saturated vaporline define the vapor bubble. These two lines connect at, what istermed, the critical point. Saturated mixtures exist only under thevapor bubble. For pressures and temperatures outside of the vaporbubble, the fluid exists as a single phase and the properties of thatfluid, such as density, enthalpy, internal energy, etc., are uniquelydefined by the pressure and temperature. For common fluids, such aswater, these properties are tabulated as finctions of pressure andtemperatures and are available through a variety of references includinga website hosted by NIST (ref:http://webbook.nist.gov/chemistry/fluid/).

For fluids at pressures and temperatures that lie within the vaporbubble, the fluids represent mixtures of the liquid and vapor phase.Although the properties of both the vapor and liquid phases are welldefined (and tabulated for known substances), the properties of themixture are no longer uniquely defined as functions of pressure andtemperature. In order to define the averaged properties of a saturatedmixture, the ratio of the vapor and liquid components of the mixturemust be defined. The quality of the mixture, in addition to the pressureand temperature, must be defined to uniquely determine the properties ofthe mixture.

Measuring the average properties of a single or multi-phase process flowis important in many industrial application since it is the massaveraged properties of the working fluid that enter directly intomonitoring the thermodynamic performance of many processes. For example,it is the difference in the flux of enthalpy of the steam mixtureflowing into and exiting from a turbine that determines the maximummechanical work that can be extracted from the working fluid, and thusis critical to determining component efficiency. However, if the steamentering or exiting the turbine were saturated, pressure and temperaturemeasurement would not sufficient to determine the specific enthalpy, butrather, a measure of the quality of the steam would be required touniquely define the thermodynamic properties of the saturated steammixture.

Note that once the quality and pressure (or temperature) of a saturatedmixture is defined, the thermodynamic properties of the mixture aredefined through mixing laws provided the properties of the liquid andvapor sates are known. For example, measuring speed of sound enables oneto determine quality, which in turn enables one to calculate enthalpy,density, and other properties of the mixture. In addition to measuringthe specific enthalpy, a measurement of the total mass is also, ingeneral, required to determine the flux of enthalpy.

There are many other situations where knowing the quality of a saturatedmixture is beneficial. For example, in a steam power plant, the qualityof the steam within the steam turbine affects blade life. Generally itis desired to operate so the quality is as high as possible throughoutthe turbine to minimize liquid water drops that will erode the metalblades. Knowing the quality at the turbine inlet and exhaust (or at theexhaust only if the inlet is super-heated) provides a means to monitorthe quality throughout the turbine. Also, to monitor plant performanceso that it can be operated at optimum conditions and to identifydegradation effects, the steam turbine thermal performance must beknown. This requires the fluid enthalpy at the inlet and exhaust of eachturbine to be known. If the fluid at either or both locations issaturated, pressure and temperature measurements alone will not beenough to determine the enthalpy. However if an additional measurementof quality is made the enthalpy is then defined. In addition, there maybe other applications in refrigeration cycles.

The ability to measure the flow rate and composition of the saturatedvapor/liquid mixtures within the conduits is an important aspect of anysystem or strategy design to optimize the performance of a system basedon saturated vapor/liquid mixtures. The industry recognizes this, andhas been developing a wide variety of technologies to perform thismeasurement. These include probe based devices, sampling devices,venturis and ultrasonic devices

This invention provides an apparatus and method to measure homogeneousand/or non-homogeneous fluids used in industrial systems having variousworking fluids to determine various parameters of the process fluid,such as the volumetric flow of the fluid, the consistency or compositionof the fluid, the density of the fluid, the Mach number of the fluid,the size of particle flowing through the fluid, the air/mass ratio ofthe fluid and/or the percentage of entrained air/gas within a liquid orslurry.

Here a novel approach to flow measurements is proposed which utilizes anon-intrusive, externally mounted sensing element that requires nomoving parts and is highly reliable. This approach is based upon signalcorrelation and/or array processing techniques of unsteady pressuremeasurements induced in an array of externally mounted sensors. Thepiezo-film sensors clamped onto the outer surface of a pipe providescircumferential averaging of the unsteady pressures within the pipe andprovide an inexpensive solution to accurately measuring the unsteadypressures. The piezo-film also have the advantage of being able to wraparound a substantial portion of the outer circumference of the pipe toprovide circumferential averaging of the unsteady pressures with thepipe.

SUMMARY OF THE INVENTION

Objects of the present invention include an apparatus having an array ofpiezoelectric film sensors mounted or clamped axially spaced to theouter surface of the pipe for measuring the unsteady pressures of asingle and multi-phase process flows within a pipe to determine at leastone parameter of the process flow.

According to the present invention, an apparatus for measuring at leastone parameter of a process flow flowing within a pipe. The apparatusincludes at least two pressure sensors disposed on the outer surface ofthe pipe at different axial locations along the pipe. Each of thepressure sensors provides a respective pressure signal indicative of apressure disturbance within the pipe at a corresponding axial position.Each of the pressure sensors includes a piezoelectric film sensor. Asignal processor, responsive to said pressure signals, provides a signalindicative of at least one parameter of the process flow flowing withinthe pipe.

The foregoing and other objects, features and advantages of the presentinvention will become more apparent in light of the following detaileddescription of exemplary embodiments thereof.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 a is a schematic illustration of an apparatus having an array ofpiezoelectric film sensors clamped onto the outer surface a pipe, inaccordance with the present invention.

FIG. 1 b is a schematic illustration of an apparatus having an array ofpiezoelectric film sensors mounted on the outer surface of a pipe, inaccordance with the present invention.

FIG. 2 is a cross-sectional view of a pipe and array of sensors showingthe turbulent structures within the pipe, in accordance with the presentinvention.

FIG. 3 is a cross-sectional view of a piezoelectric film sensor inaccordance with the present invention.

FIG. 4 is a top plan view of a piezoelectric film sensor in accordancewith the present invention.

FIG. 5 is a cross-sectional view of a portion of the piezoelectric filmsensor and clamp, in accordance with the present invention.

FIG. 6 is a cross-sectional view of a portion of the piezoelectric filmsensor and clamp, in accordance with the present invention.

FIG. 7 is a cross-sectional view of a portion of the piezoelectric filmsensor and clamp, in accordance with the present invention.

FIG. 8 is a side elevational view of a portion of the piezoelectric filmsensor and clamp showing a step in the attachment of the clamp to thepipe, in accordance with the present invention.

FIG. 9 is a side elevational view of a portion of the piezoelectric filmsensor and clamp, in accordance with the present invention.

FIG. 10 is a perspective view of a plurality of piezoelectric filmsensors clamped to a pipe having covers disposed thereover, inaccordance with the present invention.

FIG. 11 is a cross sectional end view of a piezoelectric film sensorclamped to a pipe, in accordance with the present invention.

FIG. 12 is a block diagram of a probe for measuring the speed of soundpropagating through a process flow flowing within a pipe, in accordancewith the present invention.

FIG. 13 is a plot showing the standard deviation of sound speed versusfrequency for various arrays of process flow parameter measurementsystem, in accordance with the present invention.

FIG. 14 is a kω plot of data processed from an array of pressure sensorsuse to measure the speed of sound propagating through a saturatedvapor/liquid mixture flowing in a pipe, in accordance with the presentinvention.

FIG. 15 is a block diagram of an apparatus for measuring the vorticalfield of a process flow within a pipe, in accordance with the presentinvention.

FIG. 16 is a kω plot of data processed from an apparatus embodying thepresent invention that illustrates slope of the convective ridge, and aplot of the optimization function of the convective ridge, in accordancewith the present invention.

FIG. 17 is a functional flow diagram of an apparatus embodying thepresent invention.

BEST MODE FOR CARRYING OUT THE INVENTION

Referring to FIG. 1 a, an apparatus, generally shown as 10, is providedto sense and determine specific characteristics or parameters of asingle phase fluid 12 (e.g., gas and liquid) and/or a multi-phasemixture 12 (e.g., process flow) flowing through a pipe. The multi-phasemixture may be a two-phase liquid/vapor mixture, a solid/vapor mixtureor a solid/liquid mixture, gas entrained liquid or even a three-phasemixture. As will be described in greater detail, the apparatus measuresthe speed of sound propagating through the fluid or multiphase mixtureflow to determine any one of a plurality of parameters of the flow, suchas the steam quality or “wetness”, vapor/mass ratio, liquid/solid ratio,the volumetric flow rate, the mass flow rate, the size of the suspendedparticles, density, gas volume fraction, and the enthalpy of the flow.Additionally, the apparatus 10 is capable of measuring the unsteadypressure disturbances (e.g., vortical effects, density changes) of theflow passing through the pipe to determine the velocity of the flow, andhence the volumetric flow rate of the flow.

FIG. 1 a illustrates a schematic drawing of the apparatus 10 thatincludes a sensing device 16 comprising an array of pressure sensors (ortransducers) 18-21 spaced axially along the outer surface 22 of a pipe14, having a process flow propagating therein. The pressure sensorsmeasure the unsteady pressures produced by acoustical and/or vorticaldisturbances within the pipe, which are indicative of a parameter of thesingle phase fluid or multiphase mixture 12. The output signals (P₁-P₄)of the pressure sensors 18-21 are provided to a processing unit 24,which processes the pressure measurement data and determines at leastone parameter of the flow. Such as, the characteristics and parametersdetermined may include the volumetric flow of the flow, the consistencyor composition of the flow, the density of the mixture, the Mach numberof the flow, the size of particle flowing through the mixture, theair/mass ratio of the mixture and/or the percentage of entrained air orgas within the mixture.

In an embodiment of the present invention shown in FIG. 1 a, theapparatus 10 has four pressure sensors 18-21 disposed axially along thepipe 14 for measuring the unsteady pressure P₁-P₄ of the fluid ormixture 12 flowing therethrough. The apparatus 10 has the ability tomeasure the volumetric flow rate and other flow parameters using one orboth of the following techniques described herein below:

-   -   1) Determining the speed of sound of acoustical disturbances or        sound waves propagating through the flow 12 using the array of        pressure sensors 18-21, and/or    -   2) Determining the velocity of vortical disturbances or “eddies”        propagating through the flow 12 using the array of pressure        sensors 18-21.

Generally, the first technique measures unsteady pressures created byacoustical disturbances propagating through the flow 12 to determine thespeed of sound (SOS) propagating through the flow. Knowing the pressureand/or temperature of the flow and the speed of sound of the acousticaldisturbances, the processing unit 24 can determine the mass flow rate,the consistency of the mixture (i.e., the mass/air ratio, themass/liquid ratio, the liquid/air ratio), the volumetric flow rate, thedensity of the mixture, the enthalpy of the mixture, the Mach number ofthe mixture, the size of the particles within a mixture, and otherparameters, which will be described in greater detail hereinafter.

The apparatus in FIG. 1 a also contemplates providing one or moreacoustic sources 27 to enable the measurement of the speed of soundpropagating through the flow for instances of acoustically quiet flow.The acoustic sources may be disposed at the input end of output end ofthe probe, or at both ends as shown. One should appreciate that in mostinstances the acoustics sources are not necessary and the apparatuspassively detects the acoustic ridge provided in the flow 12.

The second technique measures the velocities associated with unsteadyflow fields and/or pressure disturbances created by vorticaldisturbances or “eddies” 118 to determine the velocity of the flow 12.The pressure sensors 18-21 measure the unsteady pressures P₁-P₄ createdby the vortical disturbances as these disturbances convect within theflow 12 through the pipe 14 in a known manner, as shown in FIG. 2.Therefore, the velocity of these vortical disturbances is related to thevelocity of the mixture and hence the volumetric flow rate may bedetermined, as will be described in greater detail hereinafter.

In one embodiment of the present invention as shown in FIGS. 1 a, 1 band 2, each of the pressure sensors 18-21 may include a piezoelectricfilm sensor 30 as shown in FIGS. 3 and 4 to measure the unsteadypressures of the mixture 12 using either technique describedhereinbefore.

As best shown in FIGS. 3 and 4, the piezoelectric film sensors 30include a piezoelectric material or film 32 to generate an electricalsignal proportional to the degree that the material is mechanicallydeformed or stressed. The piezoelectric sensing element is typicallyconformed to allow complete or nearly complete circumferentialmeasurement of induced strain to provide a circumferential-averagedpressure signal. The sensors can be formed from PVDF films, co-polymerfilms, or flexible PZT sensors, similar to that described in “Piezo FilmSensors Technical Manual” provided by Measurement Specialties, Inc.,which is incorporated herein by reference. A piezoelectric film sensorthat may be used for the present invention is part number 1-1002405-0,LDT4-028K, manufactured by Measurement Specialties, Inc.

Piezoelectric film (“piezofilm”), like piezoelectric material, is adynamic material that develops an electrical charge proportional to achange in mechanical stress. Consequently, the piezoelectric materialmeasures the strain induced within the pipe 14 due to unsteady pressurevariations (e.g., vortical and/or acoustical) within the process mixture12. Strain within the pipe is transduced to an output voltage or currentby the attached piezoelectric sensor. The piezoelectrical material orfilm may be formed of a polymer, such as polarized fluoropolymer,polyvinylidene fluoride (PVDF).

FIGS. 3 and 4 illustrate a piezoelectric film sensor (similar to thesensor 18 of FIG. 1 a), wherein the piezoelectric film 32 is disposedbetween and pair of conductive coatings 34,35, such as silver ink. Thepiezoelectric film 32 and conductive coatings 34,35 are coated onto aprotective sheet 36 (e.g., mylar) with a protective coating 38 disposedon the opposing side of the upper conductive coating. A pair ofconductors 40,42 is attached to a respective conductive coating 34,35.

The thickness of the piezoelectric film 32 may be in the range of 8 umto approximately 110 um. The thickness is dependent on the degree ofsensitivity desired or needed to measure the unsteady pressures withinthe pipe 14. The sensitivity of the sensor 30 increases as the thicknessof the piezoelectric film increases.

The advantages of this technique of clamping the PVDF sensor 30 onto theouter surface of the pipe 14 are the following:

-   -   1. Non-intrusive flow rate measurements    -   2. Low cost    -   3. Measurement technique requires no excitation source. Ambient        flow noise is used as a source.    -   4. Flexible piezoelectric sensors can be mounted in a variety of        configurations to enhance signal detection schemes. These        configurations include a) co-located sensors, b) segmented        sensors with opposing polarity configurations, c) wide sensors        to enhance acoustic signal detection and minimize vortical noise        detection, d) tailored sensor geometries to minimize sensitivity        to tube modes, e) differencing of sensors to eliminate acoustic        noise from vortical signals.    -   5. Higher Operating Temperatures (125C) (co-polymers)

Referring to FIG. 1 b, the piezoelectric film sensors 30 may be mounteddirectly onto the outer diameter of the pipe 14 by epoxy, glue or otheradhesive.

Alternatively, as shown in FIGS. 5-9, the piezoelectric film sensor 30is be adhered or attached to a strap 72 which is then clamped (orstrapped) onto the outer surface of the pipe 14 at each respective axiallocation, similar to that described in U.S. Provisional Application No.60/425,436 (Cidra Docket No. CC-0538), filed Nov. 12, 2002; and U.S.Provisional Application No. 60/426,724 (Cidra Docket No. CC-0554), whichare incorporated herein by reference.

As shown in FIG. 5, the piezoelectric film sensor 30 is attached to theouter surface 73 of the strap in relation to the pipe 14. The conductiveinsulator 36 is attached to the outer surface of the strap by doubleside tape or any other appropriate adhesive. The adhesive is preferablyflexible or compliant but minimizes creep between the strap andpiezoelectric film sensor during the operation of the sensor 30. Thelength of the strap is substantially the same as the circumference ofthe pipe 14. The piezoelectric film sensor may extend over thesubstantial length of the strap or some portion less than the strap. Inthe embodiment shown in FIG. 5, the piezoelectric film sensor 30 extendssubstantially the length of the strap 72 to provide a circumferentiallyaveraged pressure signal to the processing unit 24.

Referring to FIGS. 6 and 7, an attachment assembly 75 comprising a firstattachment block 76, a second attachment block 77 and a spacer 78disposed therebetween, which are welded together to provide slots 79between each of the attachment blocks and the spacer. The slots receiverespective ends of the strap 72 to secure the ends of the straptogether. One end of the strap 72 and the pair of conductors 40,42 arethreaded through the slot disposed between the first attachment blockand the spacer. The strap 72 and conductors 40,42 are secured to theattachment assembly by a pair of fasteners 80. The other end of thestrap is threaded through the slot disposed between the spacer and thesecond attachment block. Referring to FIG. 8, the other end of the strapis pull tightly between the spacer and the second attachment to draw upand take-up the tension and securely clamp the strap to the pipe 14. Asshown in FIG. 9, a set screw 81 within the second attachment block istighten, which then pierces the other end of the strap to secure it tothe attachment assembly. The excess portion of the other end of thestrap is then cut off. The piezoelectric film sensor may then be coveredwith a copper sheet to provide a grounding shield for EMI or otherelectrical noise.

While the piezoelectric film sensor 30 was mounted to the outer surfaceof the straps 72, the present invention contemplates the piezoelectricfilm sensor may be mounted to the inner surface of the strap, therebyresulting in the piezoelectric sensor being disposed between the strapand the outer surface of the pipe 14.

FIG. 10 illustrates a protective cover 82, having two halves, clampedonto the pipe and secured together over each of the piezoelectric filmsensors 30 and straps 72. The protective cover is formed from aluminumwith thermal fins 83 molded therein to assist with dissipating heat awayfrom the sensors. The cover further includes an insulative portion 84disposed between the pipe and the aluminum portion of the cover. Theconductors and wiring thereto pass through a conduit 84 that extendsbetween each of the covers.

While the present invention illustrates separate covers for each sensor,the present invention contemplates a single cover that covers all thesensors.

Referring to FIGS. 13 and 14, an apparatus 110, similar to apparatus 10of FIG. 1 a, embodying the present invention is provided that measuresat least one parameter/characteristic of a single and/or multiphase flow12 flowing within a pipe 14. The apparatus may be configured andprogrammed to measure the speed of sound propagating through the flow 12or measure the vortical disturbances propagating through the flow 12. Insome instances, the apparatus 10 may be configured to measure both thespeed of sound and the vortical disturbances. Depending on theconfiguration or embodiment, the apparatus can measure at least one ofthe following parameters of the flow 12: the wetness or steam quality(volumetric phase fraction), the volumetric flow rate, the size of theliquid particles, the mass flow, the enthalpy and the velocity of themixture. To determine any one of these parameters, the apparatus 110measures the unsteady pressures created by the speed of sound (SOS)and/or the vortical disturbances propagating through the single phase ormultiphase flow 12 flowing in the pipe 14, which will be described ingreater detail hereinafter.

The type of unsteady pressure measurement being made determines thespacing of the sensors. Measurement of unsteady vortical pressuresrequire sensors spacing less than the coherence length of the vorticaldisturbances which is typically on the order of a pipe diameter.Correlation or array processing of the unsteady vortical pressuremeasurements between sensors is used to determine the bulk flow rate ofthe process mixture, which will be described in greater detailhereinafter.

Mass flow rates and other parameters are determined by measuring thespeed of sound propagating within the process mixture 12. Theseparameters are determined by correlating or array processing unsteadypressure variations created by acoustic disturbances within the processmixture. In this case, the wavelength of the measured acoustic signaldetermines the sensor spacing. The desired wavelength of the measuredacoustic signal is dependent upon the dispersion of particles in themixture flow, which is dependent on the particle size. The larger theparticle size is the longer the sensing device of the aperture.

As described hereinbefore, the apparatus 110 of the present inventionmay be configured and programmed to measure and process the detectedunsteady pressures P₁(t)-P_(N)(t) created by acoustic waves and/orvortical disturbances, respectively, propagating through the mixture todetermine parameters of the mixture flow 12. One such apparatus 10 isshown in FIG. 12 that measures the speed of sound (SOS) ofone-dimensional sound waves propagating through the vapor/liquid mixtureto determine the composition the mixture. The apparatus 110 is alsocapable of determining the average size of the droplets, velocity of themixture, enthalpy, mass flow, steam quality or wetness, density, and thevolumetric flow rate of the single or multi-phase flow 12. It is knownthat sound propagates through various mediums at various speeds in suchfields as SONAR and RADAR fields. The speed of sound propagating throughthe flow 12 within the pipe 14 may be determined using a number of knowntechniques, such as those set forth in U.S. patent application Ser. No.09/344,094, entitled “Fluid Parameter Measurement in Pipes UsingAcoustic Pressures”, filed Jun. 25, 1999, now U.S. Pat. No. 6,354,147;U.S. patent application Ser. No. 09/729,994, filed Dec. 4, 2002, nowU.S. Pat. No. 6,609,069; and U.S. patent application Ser. No.10/007,749, entitled “Fluid Parameter Measurement in Pipes UsingAcoustic Pressures”, filed Nov. 7, 2001, each of which are incorporatedherein by reference.

In accordance with the present invention, the speed of sound propagatingthrough the process flow 12 is measured by passively listening to theflow with an array of unsteady pressure sensors to determine the speedat which one-dimensional compression waves propagate through the flow 12contained within the pipe 14.

As shown in FIG. 13, the apparatus 110 has an array of at least threeacoustic pressure sensors 115,116,117, located at three locationsx₁,x₂,x₃ axially along the pipe 14. One will appreciate that the sensorarray may include more than three pressure sensors as depicted bypressure sensor 118 at location x_(N). The pressure generated by theacoustic waves may be measured through pressure sensors 115-118. Thepressure sensors 15-18 provide pressure time-varying signalsP₁(t),P₂(t),P₃(t),P_(N)(t) on lines 120,121,122,123 to a signalprocessing unit 130 to known Fast Fourier Transform (FFT) logics126,127,128,129, respectively. The FFT logics 126-129 calculate theFourier transform of the time-based input signals P₁(t)-P_(N)(t) andprovide complex frequency domain (or frequency based) signalsP₁(ω),P₂(ω),P₃(ω),P_(N)(ω)) on lines 132,133,134,135 indicative of thefrequency content of the input signals. Instead of FFT'S, any othertechnique for obtaining the frequency domain characteristics of thesignals P₁(t)-P_(N)(t), may be used. For example, the cross-spectraldensity and the power spectral density may be used to form a frequencydomain transfer functions (or frequency response or ratios) discussedhereinafter.

The frequency signals P₁(ω)-P_(N)(ω) are fed to a_(mix)-Mx CalculationLogic 138 which provides a signal to line 40 indicative of the speed ofsound of the multiphase mixture a_(mix) (discussed more hereinafter).The a_(mix) signal is provided to map (or equation) logic 142, whichconverts a_(mix) to a percent composition of a mixture and provides a %Comp signal to line 44 indicative thereof (as discussed hereinafter).Also, if the Mach number Mx is not negligible and is desired, thecalculation logic 138 may also provide a signal Mx to line 46 indicativeof the Mach number Mx.

More specifically, for planar one-dimensional acoustic waves in ahomogenous mixture, it is known that the acoustic pressure field P(x,t)at a location x along the pipe 14, where the wavelength λ of theacoustic waves to be measured is long compared to the diameter d of thepipe 14 (i.e., λ/d>>1), may be expressed as a superposition of a righttraveling wave and a left traveling wave, as follows:P(x, t)=(Ae ^(−ik,x) +Be ^(+ik) ¹ ^(x))e ^(iωt)  Eq. 1where A,B are the frequency-based complex amplitudes of the right andleft traveling waves, respectively, x is the pressure measurementlocation along a pipe 14, ω is frequency (in rad/sec, where ω=2πf), andk_(r),k₁ are wave numbers for the right and left traveling waves,respectively, which are defined as: $\begin{matrix}{{k_{r} \equiv {\left( \frac{\omega}{a_{mix}} \right)\frac{1}{1 + M_{x}}}}{and}\text{}{k_{l} \equiv {\left( \frac{\omega}{a_{mix}} \right)\frac{1}{1 - M_{x}}}}} & {{Eq}.\quad 2}\end{matrix}$where a_(mix) is the speed of sound of the mixture in the pipe, ω isfrequency (in rad/sec), and M_(x) is the axial Mach number of the flowof the mixture within the pipe, where: $\begin{matrix}{M_{x} \equiv \frac{V_{mix}}{a_{mix}}} & {{Eq}.\quad 3}\end{matrix}$where Vmix is the axial velocity of the mixture. For non-homogenousmixtures, the axial Mach number represents the average velocity of themixture and the low frequency acoustic field description remainssubstantially unaltered.

The data from the array of sensors 115-118 may be processed in anydomain, including the frequency/spatial domain, the temporal/spatialdomain, the temporal/wave-number domain or the wave-number/frequency(k-ω) domain. As such, any known array processing technique in any ofthese or other related domains may be used if desired, similar to thetechniques used in the fields of SONAR and RADAR.

Also, some or all of the functions within the signal processing unit 130may be implemented in software (using a microprocessor or computer)and/or firmware, or may be implemented using analog and/or digitalhardware, having sufficient memory, interfaces, and capacity to performthe functions described herein.

Acoustic pressure sensors 115-118 sense acoustic pressure signals that,as measured, are lower frequency (and longer wavelength) signals thanthose used for ultrasonic probes of the prior art, and thus the currentinvention is more tolerant to inhomogeneities in the flow, such as timeand space domain inhomogeneities within the flow.

It is within the scope of the present invention that the pressure sensorspacing may be known or arbitrary and that as few as two sensors arerequired if certain information is known about the acoustic propertiesof the process flow 12. The pressure sensors are spaced sufficientlysuch that the entire length of the array (aperture) is at least asignificant fraction of the measured wavelength of the acoustic wavesbeing measured. The acoustic wavelength to be measured in a mixture is afinction of at least the size and mass of the droplets/particles, andthe viscosity of the vapor. The greater the size and mass of thedroplets and/or the less viscous the vapor, the greater the spacing ofthe sensors is needed. Conversely, the smaller the size and mass of thedroplets/particles and/or the more viscous the vapor, the shorter thespacing of the sensors is needed. For single phase flow, the acousticwavelength is a function of the type or characteristics of flow 12.

Assuming that the droplets/particles of the mixture are small enough andthe acoustic frequencies and the frequencies of perturbations associatedwith the acoustics are low enough for the droplets/particles of liquidto exhibit negligible slip (both steady and unsteady), the sound speedcan be assumed to be substantially non-dispersive (that is constant withfrequency) and the volumetric phase fraction of the mixture could bedetermined through the Wood equation:$\rho_{mix} = {\sum\limits_{i = 1}^{N}{\phi_{i}\rho_{i}}}$$\frac{1}{\rho_{mix}a_{mix}^{2}} = {\sum\limits_{i = 1}^{N}\frac{\phi_{i}}{\rho_{i}a_{i}^{2}}}$${\sum\limits_{i = 1}^{N}\phi_{i}} = 1$

For one-dimensional waves propagating, the compliance introduced by thepipe (in this case a circular tube of modulus E, radius R and wallthickness t) reduces the measured sound speed from the infinitedimensional sound speed. The effect of the conduit is given by thefollowing relationship:$\frac{1}{\rho_{mix}c_{measured}^{2}} = {\frac{1}{\rho_{mix}c_{mix}^{2}} + \sigma}$where $\sigma \equiv \frac{2R}{Et}$

Utilizing the relations above for a vapor/liquid mixture, the speed atwhich sound travels within the representative vapor/liquid mixture is afunction of vapor/liquid mass ratio. The effect of increasing liquidfraction, i.e. decreasing vapor/liquid ratio, is to decrease the soundspeed. Physically, adding liquid droplets effectively mass loads themixture, while not appreciably changing the compressibility of the air.Over the parameter range of interest, the relation between mixture soundspeed and vapor/liquid ratio is well behaved and monatomic.

While the calibration curves based on predictions from first principlesare encouraging, using empirical data mapping from sound speed tovapor/liquid ratio may result in improved accuracy of the presentinvention to measure the vapor/liquid fractions of the mixture.

The sound speed increases with increasing frequency and asymptotestoward a constant value. The sound speed asymptote at higher frequencyis essentially the sound speed of air only with no influence of thesuspended liquid droplets. Also, it is apparent that the sound speed ofthe vapor/liquid mixture has not reached the quasi-steady limit at thelowest frequency for which sound speed was measured. The sound speed iscontinuing to decrease at the lower frequency limit. An importantdiscovery of the present invention is that the speed at which soundpropagates through droplets suspended in a continuous vapor is said tobe dispersive. As defined herein, the speed at which acoustic wavespropagate through dispersive mixtures varies with frequency.

Measuring the sound speed of a saturated vapor/liquid mixture 12 atprogressively lower and lower frequencies becomes inherently lessaccurate as the total length of the array of pressure sensors 115-118(Δx_(aperture)), which define the aperture of the array, becomes smallcompared to the wavelength of the acoustics. In general, the apertureshould be at least a significant fraction of a wavelength of the soundspeed of interest. Consequently, longer arrays are used to resolve soundspeeds at lower frequencies, which will be described in greater detailhereinafter. As shown in FIG. 14, the standard deviation associated withdetermining the speed of sound in air is shown as a function offrequency for three arrays of varying aperture, namely 1.5 ft, 3 ft and10 ft.

For accurately measuring sound speeds at ultra-low frequencies, the datasuggests that utilizing a quasi-steady model to interpret therelationship between sound speed, measured at frequencies above those atwhich the quasi-steady model is applicable, and the liquid-to-vaporratio would be problematic, and may, in fact, be impractical. Thus, thekey to understanding and interpreting the composition of vapor/liquidmixtures through sound speed measurements lies in the dispersivecharacteristics of the vapor/liquid mixture, which is described ingreater detail in U.S. patent application Ser. No. 10/412,839, filedApr. 10, 2003; U.S. patent application Ser. No. 10/349,716, filed Jan.3, 2003; and U.S. patent application Ser. No. 10/376,427, filed Feb. 26,2003, which are all incorporated herein by reference.

In accordance with the present invention the dispersive nature of thesystem utilizes a first principles model of the interaction between thevapor and liquid droplets. This model is viewed as being representativeof a class of models that seek to account for dispersive effects. Othermodels could be used to account for dispersive effects without alteringthe intent of this disclosure (for example, see the paper titled“Viscous Attenuation of Acoustic Waves in Suspensions” by R. L. Gibson,Jr. and M. N. Toksoz), which is incorporated herein by reference. Themodel allows for slip between the local velocity of the continuous vaporphase and that of the droplets. The drag force on the droplets by thecontinuous vapor is modeled by a force proportional to the differencebetween the local vapor velocity and that of the liquid droplets and isbalanced by inertial force:$F_{drag} = {{K\left( {U_{f} - U_{p}} \right)} = {\rho_{p}v_{p}\frac{\partial U_{p}}{\partial t}}}$where K=proportionality constant, U_(f)=fluid velocity, U_(p)=liquiddroplet velocity, ρ_(p)=liquid droplet density and v_(p)=particlevolume.The effect of the force on the continuous vapor phase by the liquiddroplets is modeled as a force term in the axial momentum equation. Theaxial momentum equation for a control volume of area A and length Δx isgiven by:${P_{x} - P_{x + {\Delta\quad x}} - {{K\left( {U_{f} - U_{p}} \right)}\left\{ \frac{\phi_{p}\Delta\quad x}{v_{p}} \right\}}} = {\frac{\partial}{\partial t}\left( {\rho_{f}U_{f}\Delta\quad x} \right)}$where P=pressure at locations x and Δx, φ_(p)=volume fraction of theliquid droplets, p_(f)=vapor density.

The droplet drag force is given by:$F_{drag} = {{K\left( {U_{f} - U_{p}} \right)} = {C_{d}A_{p}\frac{1}{2}{\rho_{f}\left( {U_{f} - U_{p}} \right)}^{2}}}$where C_(d)=drag coefficient, A_(p)=frontal area of liquid droplet andρ_(f)=vapor density.

Using Stokes law for drag on a sphere at low Reynold's number gives thedrag coefficient as:$C_{d} = {\frac{24}{Re} = \frac{24\mu}{{\rho_{f}\left( {U_{f} - U_{p}} \right)}D_{p}}}$where D_(p)=droplet diameter and μ=vapor viscosity.

Solving for K in this model yields:K=3πμD _(p)

Using the above relations and 1-dimensional acoustic modelingtechniques, the following 5relation can be derived for the dispersivebehavior of an idealized vapor/liquid mixture.${a_{mix}(\omega)} = {a_{f}\sqrt{\frac{1}{1 + \frac{\varphi_{p}\rho_{p}}{\rho_{f}\left( {1 + {\omega^{2}\frac{\rho_{p}^{2}v_{p}^{2}}{K^{2}}}} \right)}}}}$

In the above relation, the fluid SOS, density (ρ) and viscosity (φ) arethose of the pure phase fluid, v_(p) is the volume of individualdroplets and φ_(p) is the volumetric phase fraction of the droplets inthe mixture. These relationships to determine droplet size and liquid tovapor mass ratio are described in U.S. patent application Ser. No.10/412,839, filed Apr. 10, 2003; U.S. patent application Ser. No.10/349,716, filed Jan. 3, 2003; and U.S. patent application Ser. No.10/376,427, filed Feb. 26, 2003, which are all incorporated herein byreference.

The apparatus 10 further includes the ability to measure of volumetricflow rate of the mixture by comparing the difference of the speed of onedimensional sound waves propagating with and against the mean flow.

This method of determining the volumetric flow rate of the flow 12relies on the interaction of the mean flow with the acoustic pressurefield. The interaction results in sound waves propagating with the meanflow traveling at the speed of sound (if the vapor/liquid mixture werenot flowing) plus the convection velocity and, conversely, sound wavestraveling against the mean flow propagating at the speed of sound minusthe convection velocity. That is,α_(R)=α_(mix) +uα_(L)=α_(mix) −uwhere a_(R)=velocity of a right traveling acoustic wave relative to astationary observer (i.e. the tube 14), a_(L)=velocity of a lefttraveling acoustic wave apparent to a stationary observer, a_(mix)=speedof sound traveling through the mixture (if the mixture was not flowing)and u=the mean flow velocity (assumed to be flowing from left to rightin this instance). Combining these two equations yields an equation forthe mean velocity, $u = \frac{a_{R} - a_{L}}{2}$Therefore, by measuring the propagation velocity of acoustic waves inboth directions relative to the pipe 14 as described hereinbefore, themean flow velocity can be calculated by multiplying the mean flowvelocity by the cross-sectional area of the pipe 14.

The practicality of using this method to determine the mean flow ispredicated on the ability to resolve the sound speed in both directionswith sufficient accuracy to determine the volumetric flow.

For the sound speed measurement, the apparatus 10 utilizes similarprocessing algorithms as those employed herein before, and described ingreater detail hereinafter. The temporal and spatial frequency contentof sound propagating within the pipe 14 is related through a dispersionrelationship. $\omega = \frac{k}{a_{mix}}$The wave number is k, which is defined as k=2π/λ, ω is the temporalfrequency in rad/sec, and a_(mix) is the speed at which sound propagateswithin the process piping. For this cases where sound propagates in bothdirections, the acoustic power is located along two acoustic ridges, onefor the sound traveling with the flow at a speed of a_(mix)+V_(mix) andone for the sound traveling against the flow at a speed ofa_(mix)−V_(mix).

Further, FIG. 14 illustrates the ability of the present invention todetermine the velocity of a fluid moving in a pipe. The color contoursrepresent the relative signal power at all combinations of frequency andwavenumber. The highest power “ridges” represent the acoustic wave withslope of the ridges equal to the propagation speed. Note that theacoustic ridges “wrap” to the opposite side of the plot at the spatialNyquist wavenumber equal to ±3.14 in this case (i.e. the acoustic ridgethat slopes up and to the right starting at the bottom of the plot, theright-side ridge, wraps to the left side of the plot at approximately550 Hz and continues sloping up and to the right). The dashed lines showthe best-fit two-variable maximization of the power with the twovariables being sound speed and flow velocity. The right-side ridgerepresents the acoustic wave traveling in the same direction as the bulkflow and therefore its slope is steeper than the left-side ridge thatrepresents the acoustic wave traveling in the opposite direction of theflow. This indicates that the acoustic wave traveling in the samedirection of the flow is traveling faster than the acoustic wavetraveling in the opposite direction of the flow relative to thestationary sensors located on the probe.

Referring to FIG. 1 a, an apparatus 10 embodying the present inventionincludes the ability to measure volumetric flow rate of the mixture bymeasuring the unsteady pressures generated by vortical disturbancepropagating in the mixture. The apparatus 10 uses one or both of thefollowing techniques to determine the convection velocity of thevortical disturbances within the process flow 12 by:

-   -   1) Cross-correlating unsteady pressure variations using an array        of unsteady pressure sensors.    -   2) Characterizing the convective ridge of the vortical        disturbances using an array of unsteady pressure sensors.

The overwhelming majority of industrial process flows involve turbulentflow. Turbulent fluctuations within the process flow govern many of theflow properties of practical interest including the pressure drop, heattransfer, and mixing. For engineering applications, considering only thetime-averaged properties of turbulent flows is often sufficient fordesign purposes. For sonar flow metering technology, understanding thetime-averaged velocity profile in turbulent flow provides a means tointerpret the relationship between speed at which coherent structuresconvect and the volumetrically averaged flow rate.

From the saturated vapor/liquid mixture mechanics perspective, thismethod relies on the ability of the apparatus 10 to isolate theconvective pressure field (which convects at or near the mean velocityof the saturated vapor/liquid mixture) from the acoustic pressure field(which propagates at the at the speed of sound). In this sense, thevelocity measurement is independent of the sound speed measurement.

For turbulent flows 12, the time-averaged axial velocity varies withradial position from zero at the wall to a maximum at the centerline ofthe pipe 14. The flow near the wall is characterized by steep velocitygradients and transitions to relatively uniform core flow near thecenter of the pipe 14. FIG. 2 shows a representative schematic of avelocity profile and coherent vortical flow structures 188 present infully developed turbulent flow 12. The vortical structures 188 aresuperimposed over time averaged velocity profile within the pipe 14 andcontain temporally and spatially random fluctuations with magnitudestypically less than 10% percent of the mean flow velocity.

From a volumetric flow measurement perspective, the volumetricallyaveraged flow velocity is of interest. The volumetrically averaged flowvelocity, defined as V=Q/A, is a useful, but arbitrarily definedproperty of the flow. Here, A is the cross sectional area of the tubeand Q is the volumetric flow rate. In fact, given the velocity profilewithin the tube, little flow is actually moving at this speed.

Turbulent pipe flows 12 are highly complex flows. Predicting the detailsof any turbulent flow is problematic, however, much is known regardingthe statistical properties of the flow. For instance, turbulent flowscontain self-generating, coherent vortical structures often termed“turbulent eddies”. The maximum length scale of these eddies is set bythe diameter of the pipe 14. These structures remain coherent forseveral tube diameters downstream, eventually breaking down intoprogressively smaller eddies until the energy is dissipated by viscouseffects.

Experimental investigations have established that eddies generatedwithin turbulent boundary layers convect at roughly 80% of maximum flowvelocity. For tube flows, this implies that turbulent eddies willconvect at approximately the volumetrically averaged flow velocitywithin the pipe 14. The precise relationship between the convectionspeed of turbulent eddies and the flow rate for each class of meters canbe calibrated empirically as described below.

The apparatus 170 of FIG. 15 determines the convection velocity of thevortical disturbances within the flow by cross correlating unsteadypressure variations using an array of unsteady pressure sensors, similarto that shown in U.S. patent application Ser. No. 10/007,736, filed Nov.8, 2001, entitled “Flow Rate Measurement Using Unsteady Pressures”,which is incorporated herein by reference.

Referring to FIG. 15, the apparatus 170 includes a sensing section 172along a pipe 14 and a signal processing unit 174. The pipe 14 has twomeasurement regions 176,178 located a distance ΔX apart along the pipe14. At the first measurement region 176 are two unsteady (or dynamic orac) pressure sensors 180,182, located a distance X₁ apart, capable ofmeasuring the unsteady pressure in the pipe 14, and at the secondmeasurement region 178, are two other unsteady pressure sensors 84,86,located a distance X₂ apart, capable of measuring the unsteady pressurein the pipe 14. Each pair of pressure sensors 180,182 and 184,186 act asspatial filters to remove certain acoustic signals from the unsteadypressure signals, and the distances X₁,X₂ are determined by the desiredfiltering characteristic for each spatial filter, as discussedhereinafter.

The apparatus 170 of the present invention measures velocitiesassociated with unsteady flow fields and/or pressure disturbancesrepresented by 188 associated therewith relating to turbulent eddies (orvortical flow fields), inhomogeneities in the flow, or any otherproperties of the flow, liquid, vapor, or pressure, having time varyingor stochastic properties that are manifested at least in part in theform of unsteady pressures. The vortical flow fields are generatedwithin the flow of the pipe 14 by a variety of non-discrete sources suchas remote machinery, pumps, valves, elbows, as well as the fluid ormixture flow itself. It is this last source, the fluid flowing withinthe pipe, that is a generic source of vortical flow fields primarilycaused by the shear forces between the flow 12 and the wall of the tubethat assures a minimum level of disturbances for which the presentinvention takes unique advantage. The flow generated vortical flowfields generally increase with mean flow velocity and do not occur atany predeterminable frequency. As such, no external discretevortex-generating source is required within the present invention andthus may operate using passive detection. It is within the scope of thepresent that the pressure sensor spacing may be known or arbitrary andthat as few as two sensors are required if certain information is knownabout the acoustic properties of the system as will be more fullydescribed herein below.

The vortical flow fields 188 are, in general, comprised of pressuredisturbances having a wide variation in length scales and which have avariety of coherence length scales such as that described in thereference “Sound and Sources of Sound”, A. P. Dowling et al, HalstedPress, 1983, which is incorporated by reference to the extend ofunderstanding the invention. Certain of these vortical flow fields 188convect at or near, or related to the mean velocity of at least one ofthe elements within a mixture flowing through the pipe 14. The vorticalpressure disturbances 188 that contain information regarding convectionvelocity have temporal and spatial length scales as well as coherencelength scales that differ from other disturbances in the flow. Thepresent invention utilizes these properties to preferentially selectdisturbances of a desired axial length scale and coherence length scaleas will be more fully described hereinafter. For illustrative purposes,the terms vortical flow field and vortical pressure field will be usedto describe the above-described group of unsteady pressure fields havingtemporal and spatial length and coherence scales described herein.

Also, some or all of the functions within the signal processing unit 174may be implemented in software (using a microprocessor or computer)and/or firmware, or may be implemented using analog and/or digitalhardware, having sufficient memory, interfaces, and capacity to performthe functions described herein.

In particular, in the processing unit 174, the pressure signal P₁(t) onthe line 190 is provided to a positive input of a summer 200 and thepressure signal P₂(t) on the line 191 is provided to a negative input ofthe summer 200. The output of the summer 200 is provided to line 204indicative of the difference between the two pressure signals P₁,P₂(e.g., P₁-P₂=P_(as1)).

The pressure sensors 180,182 together with the summer 200 create aspatial filter 176. The line 204 is fed to bandpass filter 208, whichpasses a predetermined passband of frequencies and attenuatesfrequencies outside the passband. In accordance with the presentinvention, the passband of the filter 208 is set to filter out (orattenuate) the dc portion and the high frequency portion of the inputsignals and to pass the frequencies therebetween. Other passbands may beused in other embodiments, if desired. Passband filter 208 provides afiltered signal P_(asf)l on a line 212 to Cross-Correlation Logic 216,described hereinafter.

The pressure signal P₃(t) on the line 192 is provided to a positiveinput of a summer 202 and the pressure signal P₄(t) on the line 193 isprovided to a negative input of the summer 202. The pressure sensors83,84 together with the summer 202 create a spatial filter 178. Theoutput of the summer 202 is provided on a line 206 indicative of thedifference between the two pressure signals P₃,P₄ (e.g., P₃−P₄=P_(as2)).The line 206 is fed to a bandpass filter 210, similar to the bandpassfilter 108 discussed hereinbefore, which passes frequencies within thepassband and attenuates frequencies outside the passband. The filter 210provides a filtered signal P_(asf) 2 on a line 214 to theCross-Correlation Logic 216. The signs on the summers 200,202 may beswapped if desired, provided the signs of both summers are swappedtogether. In addition, the pressure signals P₁,P₂,P₃,P₄ may be scaledprior to presentation to the summers 200,202.

The Cross-Correlation Logic 216 calculates a known time domaincross-correlation between the signals P_(asf1) and P_(asf2) on the lines212,214, respectively, and provides an output signal on a line 218indicative of the time delay τ it takes for an vortical flow field 188(or vortex, stochastic, or vortical structure, field, disturbance orperturbation within the flow) to propagate from one sensing region 176to the other sensing region 178. Such vortical flow disturbances, as isknown, are coherent dynamic conditions that can occur in the flow whichsubstantially decay (by a predetermined amount) over a predetermineddistance (or coherence length) and convect (or flow) at or near theaverage velocity of the fluid flow. As described above, the vorticalflow field 188 also has a stochastic or vortical pressure disturbanceassociated with it. In general, the vortical flow disturbances 188 aredistributed throughout the flow, particularly in high shear regions,such as boundary layers (e.g., along the inner wall of the tube 14) andare shown herein as discrete vortical flow fields 188. Because thevortical flow fields (and the associated pressure disturbance) convectat or near the mean flow velocity, the propagation time delay τ isrelated to the velocity of the flow by the distance ΔX between themeasurement regions 176,178, as discussed hereinafter.

Referring to FIG. 15, a spacing signal ΔX on a line 220 indicative ofthe distance ΔX between the sensing regions 176,178 is divided by thetime delay signal τ on the line 218 by a divider 222 which provides anoutput signal on the line 196 indicative of the convection velocityU_(c)(t) of the saturated vapor/liquid mixture flowing in the pipe 14,which is related to (or proportional to or approximately equal to) theaverage (or mean) flow velocity U_(f)(t) of the flow 12, as definedbelow:U _(c)(t)=ΔX/τ∝U _(f) (t)  Eq. 1

The present invention uses temporal and spatial filtering toprecondition the pressure signals to effectively filter out the acousticpressure disturbances P_(acoustic) and other long wavelength (comparedto the sensor spacing) pressure disturbances in the tube 14 at the twosensing regions 176,178 and retain a substantial portion of the vorticalpressure disturbances P_(vortical) associated with the vortical flowfield 188 and any other short wavelength (compared to the sensorspacing) low frequency pressure disturbances P_(other). In accordancewith the present invention, if the low frequency pressure disturbancesP_(other) are small, they will not substantially impair the measurementaccuracy of P_(vortical).

The second technique of determining the convection velocity of thevortical disturbances within the flow 12 is by characterizing theconvective ridge of the vortical disturbances using an array of unsteadypressure sensors, similar to that shown in U.S. patent application Ser.No. 09/729,994, filed Dec. 4, 2000, entitled “Method and Apparatus forDetermining the Flow Velocity Within a Pipe”, which is incorporatedherein by reference.

The sonar flow metering methodology uses the convection velocity ofcoherent structure with turbulent pipe flows 12 to determine thevolumetric flow rate. The convection velocity of these eddies 188 isdetermined by applying sonar arraying processing techniques to determinethe speed at which the eddies convect past an axial array of unsteadypressure measurements distributed along the pipe 14.

The sonar-based algorithms determine the speed of the eddies 188 bycharacterizing both the temporal and spatially frequency characteristicsof the flow field. For a train of coherent eddies convecting past afixed array of sensors, the temporal and spatial frequency content ofpressure fluctuations are related through the following relationship:$\omega = \frac{k}{U_{convect}}$Here k is the wave number, defined as k=2π/λ and has units of l/length,ω is the temporal frequency in rad/sec, and U_(convect) is theconvection velocity. Thus, the shorter the wavelength (larger k) is, thehigher the temporal frequency.

In sonar array processing, the spatial/temporal frequency content oftime stationary sound fields are often displayed using “k-ω plots”. K-ωplots are essentially three-dimensional power spectra in which the powerof a sound field is decomposed into bins corresponding to specificspatial wave numbers and temporal frequencies. On a k-ω plot, the powerassociated with a pressure field convecting with the flow is distributedin regions, which satisfies the dispersion relationship developed above.This region is termed “the convective ridge” (Beranek, 1992) and theslope of this ridge on a k-ω plot indicates the convective velocity ofthe pressure field. This suggests that the convective velocity ofturbulent eddies, and hence flow rate within a tube, can be determinedby constructing a k-ω plot from the output of a phased array of sensorand identifying the slope of the convective ridge.

FIG. 16 shows an example of a k-ω plot generated from a phased array ofpressure sensors. The power contours show a well-defined convectiveridge. A parametric optimization method was used to determine the “best”line representing the slope of the convective ridge 200. For this case,a slope of 14.2 ft/sec was determined. The intermediate result of theoptimization procedure is displayed in the insert, showing thatoptimized value is a unique and well-defined optima.

The k-w plot shown in FIG. 16 illustrates the fundamental principlebehind sonar based flow measure, namely that axial arrays of pressuresensors can be used in conjunction with sonar processing techniques todetermine the speed at which naturally occurring turbulent eddiesconvect within a pipe.

The present invention will now be described with reference to FIG. 17wherein the discussions based on the calculation of various parametersand properties are detailed herein above with reference to the variousFigures. In accordance with the present invention utilizing a probe10,110,170 to determine the speed of sound propagating through a flow12, such as a mixture, provides various specific properties of a mixtureand the velocity of the mixture and further utilizing logic comprisinginformation about the flow 12 based on the measured parameters. Thesteady state pressure and temperature of the mixture may be measured byany known or contemplated method as represented by 270 from whichvarious fluid properties may be determined from tables or graphs of theknown relationships for speed of sound and density for the two phases ofthe mixture as represented by 271. The speed of sound propagatingthrough the mixture is determined by the apparatus 10,110,170 of thepresent invention as set forth herein above and represented by 272. Thequality of the saturated vapor/liquid mixture is determined from thefluid properties of 271 combined with the mixture speed of sound 272using the Wood equation (or similar) as set forth herein above andrepresented by 273. The present invention also enables the determinationof other properties of the mixture such as enthalpy and density as setforth by 274 by combining the fluid properties of 271 with the qualityor composition of the mixture from 273. The present invention furtherenables the determination of the velocity of the mixture by the methodsdescribed herein above as represented by 275. The total volumetric flowrate of the mixture is thereby determined as represented by 276 and whencombined with the parameters of other properties of the mixture such asenthalpy and density as set forth by 274 various flux rates of themixture such as enthalpy and mass flow rates are enabled as representedby 277.

Another embodiment of the present invention include a pressure sensorsuch as pipe strain sensors, accelerometers, velocity sensors ordisplacement sensors, discussed hereinafter, that are mounted onto astrap to enable the pressure sensor to be clamped onto the pipe. Thesensors may be removable or permanently attached via known mechanicaltechniques such as mechanical fastener, spring loaded, clamped, clamshell arrangement, strapping or other equivalents. These certain typesof pressure sensors, it may be desirable for the pipe 12 to exhibit acertain amount of pipe compliance.

Instead of single point pressure sensors 18-21, at the axial locationsalong the pipe 12, two or more pressure sensors may be used around thecircumference of the pipe 12 at each of the axial locations. The signalsfrom the pressure sensors around the circumference at a given axiallocation may be averaged to provide a cross-sectional (or circumference)averaged unsteady acoustic pressure measurement. Other numbers ofacoustic pressure sensors and annular spacing may be used. Averagingmultiple annular pressure sensors reduces noises from disturbances andpipe vibrations and other sources of noise not related to theone-dimensional acoustic pressure waves in the pipe 12, thereby creatinga spatial array of pressure sensors to help characterize theone-dimensional sound field within the pipe 12.

The pressure sensors 18-21 of FIG. 1 a described herein may be any typeof pressure sensor, capable of measuring the unsteady (or ac or dynamic) pressures within a pipe 14, such as piezoelectric, optical,capacitive, resistive (e.g., Wheatstone bridge), accelerometers (orgeophones), velocity measuring devices, displacement measuring devices,etc. If optical pressure sensors are used, the sensors 18 - 21 may beBragg grating based pressure sensors, such as that described in U.S.patent application Ser. No. 08/925,598, entitled “High Sensitivity FiberOptic Pressure Sensor For Use In Harsh Environments”, filed Sep. 8,1997, now U.S. Pat. No. 6,016,702, and in U.S. patent application Ser.No. 10/224,821, entitled “Non-Intrusive Fiber Optic Pressure Sensor forMeasuring Unsteady Pressures within a Pipe”, which are incorporatedherein by reference. In an embodiment of the present invention thatutilizes fiber optics as the pressure sensors 14 they may be connectedindividually or may be multiplexed along one or more optical fibersusing wavelength division multiplexing (WDM), time division multiplexing(TDM), or any other optical multiplexing techniques.

It is also within the scope of the present invention that any otherstrain sensing technique may be used to measure the variations in strainin the tube, such as highly sensitive piezoelectric, electronic orelectric, strain gages attached to or embedded in the tube 14.

In certain embodiments of the present invention, a piezo-electronicpressure transducer may be used as one or more of the pressure sensors15-18 and it may measure the unsteady (or dynamic or ac) pressurevariations inside the tube 14 by measuring the pressure levels inside ofthe tube. In an embodiment of the present invention, the sensors 14comprise pressure sensors manufactured by PCB Piezotronics. In onepressure sensor there are integrated circuit piezoelectric voltagemode-type sensors that feature built-in microelectronic amplifiers, andconvert the high-impedance charge into a low-impedance voltage output.Specifically, a Model 106B manufactured by PCB Piezotronics is usedwhich is a high sensitivity, acceleration compensated integrated circuitpiezoelectric quartz pressure sensor suitable for measuring low pressureacoustic phenomena in hydraulic and pneumatic systems. It has the uniquecapability to measure small pressure changes of less than 0.001 psiunder high static conditions. The 106B has a 300 mV/psi sensitivity anda resolution of 91 dB (0.0001 psi).

The pressure sensors incorporate a built-in MOSFET microelectronicamplifier to convert the high-impedance charge output into alow-impedance voltage signal. The sensor is powered from aconstant-current source and can operate over long coaxial or ribboncable without signal degradation. The low-impedance voltage signal isnot affected by triboelectric cable noise or insulationresistance-degrading contaminants. Power to operate integrated circuitpiezoelectric sensors generally takes the form of a low-cost, 24 to 27VDC, 2 to 20 mA constant-current supply. A data acquisition system ofthe present invention may incorporate constant-current power fordirectly powering integrated circuit piezoelectric sensors.

Most piezoelectric pressure sensors are constructed with eithercompression mode quartz crystals preloaded in a rigid housing, orunconstrained tourmaline crystals. These designs give the sensorsmicrosecond response times and resonant frequencies in the hundreds ofkHz, with minimal overshoot or ringing. Small diaphragm diameters ensurespatial resolution of narrow shock waves.

The output characteristic of piezoelectric pressure sensor systems isthat of an AC-coupled system, where repetitive signals decay until thereis an equal area above and below the original base line. As magnitudelevels of the monitored event fluctuate, the output remains stabilizedaround the base line with the positive and negative areas of the curveremaining equal.

It is also within the scope of the present invention that any strainsensing technique may be used to measure the variations in strain in thepipe, such as highly sensitive piezoelectric, electronic or electric,strain gages and piezo-resistive strain gages attached to the pipe 12.Other strain gages include resistive foil type gages having a race trackconfiguration similar to that disclosed U.S. patent application Ser. No.09/344,094, filed Jun. 25, 1999, now U.S. Pat. No. 6,354,147, which isincorporated herein by reference. The invention also contemplates straingages being disposed about a predetermined portion of the circumferenceof pipe 12. The axial placement of and separation distance ΔX₁, ΔX₂between the strain sensors are determined as described herein above.

It should be understood that any of the features, characteristics,alternatives or modifications described regarding a particularembodiment herein may also be applied, used, or incorporated with anyother embodiment described herein.

Although the invention has been described and illustrated with respectto exemplary embodiments thereof, the foregoing and various otheradditions and omissions may be made therein and thereto withoutdeparting from the spirit and scope of the present invention.

1. An apparatus for measuring at least one parameter of a process flowflowing within a pipe, the apparatus comprising: at least two strainsensors attached onto the outer surface of the pipe at different axiallocations along the pipe, each of the strain sensors providing arespective strain signal indicative of a pressure disturbance within thepipe at a corresponding axial position, each of the strain sensorscomprising piezoelectric film material having a pair of conductorsdisposed on opposing surfaces of the piezoelectric material; and asignal processor, responsive to said strain signals, which provides asignal indicative of at least one parameter of the process flow flowingwithin the pipe.
 2. The apparatus of claim 1, wherein the process flowis one of a single phase fluid and a multi-phase mixture.
 3. Theapparatus of claim 1, wherein the piezoelectric film material includesat least one of polyvinylchlorine fluoride (PDVF), polymer film andflexible PZT.
 4. The apparatus of claim 1, wherein each of the pairs ofthe conductors is a coating of silver ink.
 5. The apparatus of claim 1,wherein the piezoelectric film material extends around a substantialportion of the circumference of the pipe.
 6. The apparatus of claim 1,wherein the piezoelectric film material has a thickness greater than 8mm.
 7. The apparatus of claim 1, wherein the piezoelectric film materialhas a thickness between 8 mm and 120 mm.
 8. The apparatus of claim 1,wherein the strain signals are indication of acoustic pressurespropagating within the pipe.
 9. The apparatus of claim 1, wherein theparameter of the fluid is one of steam quality or “wetness”, vapor/massratio, liquid/solid ratio, volumetric flow rate, mass flow rate, size ofsuspended particles, density, gas volume fraction, and enthalpy of theflow.
 10. The apparatus of claim 1, wherein the signal processordetermines the slope of an acoustic ridge in the k-ω plane to determinea parameter of the process flow flowing in the pipe.
 11. The apparatusof claim 1, wherein the strain signals are indication of vorticaldisturbances within the fluid flow.
 12. The apparatus of claim 11,wherein the parameter of the fluid is one of velocity of the processflow and the volumetric flow of the process fluid.
 13. The apparatus ofclaim 1, wherein the signal processor determines the slope of aconvective ridge in the k-ω plane to determine the velocity of the fluidflowing in the pipe.
 14. The apparatus of claim 1, wherein the signalprocessor determines the volumetric flow rate of the fluid flowing inthe pipe in response to the velocity of the fluid.
 15. The apparatus ofclaim 1, wherein the signal processor generates a flow velocity signalindicative of the velocity of the fluid flowing within the pipe bycross-correlating the strain signals.
 16. The apparatus of claim 1wherein each sensor measures an acoustic pressure and provides a signalindicative of an acoustic noise within the pipe.
 17. The apparatus ofclaim 1 further comprising at least three of said strain sensors. 18.The apparatus of claim 1, wherein the strain sensors are mounted to theouter surface of the pipe by an adhesive.
 19. The apparatus of claim 1,wherein the strain sensors include pressure sensors.
 20. An apparatusfor measuring at least one parameter of a process flow flowing within apipe, the apparatus comprising: at least two strain sensors attachedonto the outer surface of the pipe at different axial locations alongthe pipe, each of the strain sensors providing a respective strainsignal indicative of a pressure disturbance within the pipe at acorresponding axial position, each of the strain sensors comprisingpiezoelectric film material having a pair of conductors disposed onopposing surfaces of the piezoelectric material and an electricalinsulator disposed between each sensor and the pipeand a signalprocessor, responsive to said strain signals, which provides a signalindicative of at least one parameter of the process flow flowing withinthe pipe.